Question

4/x+3/y=1 ,6/x-15/y=8​

Answer 1

Question:-

Solve the equations simultaneously:

$\frac{4}{x} + \frac{3}{y} = 1$

$\frac{6}{x} - \frac{15}{y} = 8$

Solution:-

Let

$\frac{1}{x} = a$ and $\frac{1}{y} = b$

$4a + 3b = 1$___________(1)

$6a - 15b = 8$_________(2)

Multiply (1) with 5

$20a + 15b = 5$________(3)

Now solve (3) and (2)

$\: \: 20a + 15b = 5$

$( +)6a - 15b = 8$

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$\: \: 26a = 8$

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a = 8/26 = 4/13

So,

$\frac{1}{x} = \frac{ 4}{13}$

$x = \frac{13 }{4}$

And now take (1) and substitute the value of a and find b

$4( \frac{ 13}{4} ) +3b = 1$

$13 + 3b = 1$

$3b = 1- 13$

$3b = -12$

$b = \frac{-12}{3}$

$b = -4$

So

$\frac{1}{y} = -4$

$y = \frac{-1}{4}$